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Abstract

Addition is the most primitive arithmetic operation in digital computation. Other arithmetic operations such as subtraction, multiplication, and division can all be performed by addition together with some logic operations. With the binary number system, addition speed is inevitably limited by the carry-propagation schemes. On the other hand, carry-free addition is possible when the modified signed-digit (MSD) number representation is used. We propose a novel optoelectronic scheme to handle the parallel MSD addition and subtraction operations. An optoelectronic shared content-addressable memroy is introduced. The shared content-addressable memory uses free-space optical processing to handle the large amount of parallel memory access operations and uses electronics to postprocess and derive logic decisions. We analyze the accuracy that the required optical hardware can deliver by using a statistical cross-talk-rate model that we propose. We also evaluate other important device and system performance parameters, such as the memory capacity or the maximum number of parallel bits the adder can handle in terms of a given cross-talk rate at a certain repetition rate, the corresponding diffraction-limited memory density, and the system’s power efficiency. To confirm the underlining operational principles of the proposed optoelectronic shared content-addressable-memory MSD adder, we design and perform initial experiments for handling 8-bit MSD number addition and subtraction and present the results.

References

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Table 1

ai, Diffraction order; xi, distance from the origin of the main lobe; yi, normalized light intensity of the ith diffraction sidelobe.

Table 2

Parameters, Used for Cross-Talk-Rate Simulations

a

Rd/R

σd/R

CTR (M = 12)

2w

26/19

0.08/0.12

10−2

3w

46/31

0.03/0.045

10−5

4w

69/46

0.02/0.03

10−16

5w

92/61

0.015/0.022

10−22

aw, Half-width of the main diffraction lobe; a, mask cell’s aperture width; R, ratio of the high and the low light intensities; Rd, intensity ratio caused by the mask diffraction; σ, deviation of the intensity distribution of the low and the high levels; σd, deviation caused by mask diffractions; CTR, the cross-talk rate for the matrix dimension M = 12.

Tables (2)

Table 1

ai, Diffraction order; xi, distance from the origin of the main lobe; yi, normalized light intensity of the ith diffraction sidelobe.

Table 2

Parameters, Used for Cross-Talk-Rate Simulations

a

Rd/R

σd/R

CTR (M = 12)

2w

26/19

0.08/0.12

10−2

3w

46/31

0.03/0.045

10−5

4w

69/46

0.02/0.03

10−16

5w

92/61

0.015/0.022

10−22

aw, Half-width of the main diffraction lobe; a, mask cell’s aperture width; R, ratio of the high and the low light intensities; Rd, intensity ratio caused by the mask diffraction; σ, deviation of the intensity distribution of the low and the high levels; σd, deviation caused by mask diffractions; CTR, the cross-talk rate for the matrix dimension M = 12.